were deployed around Ampere Seamount and Cape St. Vincent, Portugal. Salinity profiles have been ...... + (alO + t*( all + t*a12 ))*p*p*p; b. 1=factor; d. =uypure.
Gljf of Cacmrz Exped:icn Contnbution Number 3
~0
XBT and XSV Data from the Gulf of Cadiz Expedition: R!V Oceanus Cruise 202
by Maureen A. Kenne,y
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APPENDIX D Profiles of Sound Speed versus Pressure Type 02 XSV depths were corrected and converted to pressure in the following manner.'First, -wesolved for time of fall by inverting the fall rate equation to obtain t
-pcall + Npcall2 - 4(pcal2)(pcal0 + XSV depth) 2pcal2
where these pcal's are Sippican's XSV fall rate coefficients and have the values pcal0 = 0.0 pcall = 5.5895 pcal2 = -0.00147. Then we computed the new depth from time. New XSV depth =-[(pcal0 + (pcall x t) + (pcal2 x :2)], where these pcal's are the Cadiz cruise XSV coefficients determined in Section 5.1 and have the values
pcal0 = 3.38 pcall = 5.8561 pcal2 = - 0.000883. The "new XSV depths" were then converted to pressure in the same manner as the XBT depths. The type 03 XSV depths were not corrected; only the conversion to pressure was made. The sound speeds for both the type 02s and 03s were adjusted by adding 0.2 m s . The data were then gridded into 2 dbar values. The graphs have been terminated at the end of good data.
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0 0
to
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0 0) 0
C) 0 oa
0 0 (V
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0
(ieqp) ejflssGJd
C\J
C)
(V
*.j
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x/ /
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0
E
Va C
L.L
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cl0
00 0 CID
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a)
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TR 8920
E21
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TR 8920
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APPENDIX F Algorithm-for Computing Salinity from Temperature, Sound Speed, and Pressure
I
Chen and Millero (1977) give an empirical relation for computing the sound speed in seawater from the measured values of the seawater temperature, salinity, and pressure. To estimate the salinity of the seawater from measured values of sound velocity, temperature, and pressure, their relation is inverted, so that salinity is found as a function of the other three variables. Chen and Millero (Eq. 4) give (U p
-
U~H 20 ) -H(U - U°2o)
=
AS + BS
1 "5
+ CS 2
where up
=
speed of sound in seawa:sr speed of sound in pure water
U° Uo
=
speed of sound in seawater at zero pressure speed of sound in pure water at zero pressure
S A, B, C
=
H=
=
=
salinity coefficients.
The term U°0 - U° 20 is also given as a function of S, S1 5, and S2 Solving for S, the equation can be rearranged as CS 2 + BS'
5
+ AS - (U p - Up)+(U -
2
)=
or
S2 + a S1 5 + bS + d = 0.
The coefficients a, b, and d are computed from parameters given by Chen and Millero. The following is a function written in C which, when given values of sound speed, temperature, and pressure, will return a value of salinity obtained by numerically solving the above equation. The program that calls the function is not given.
TR 8920
F1
sfsvel.c'
** **
C.-T. Chen and F.J. Millero (1977) Journal of the Acoustic Society of America Vol 62, pp 1129-1135. ( inversion of their equations
Source ** ** **
**
0 ) sfsvel( 1521.46, 20., sfsvel( 1506.34, 10., 1000 ) sfsvel( 1503.87, 5., 2000 )
Check values ** **
/*
= = =
35.0 35.0 35.0
Equation (4) in Chen and Millero is
--
uO - uOpure ) = A*S +B*SA1.5 +C*S^2
u - upure )-( where u upure uO uOpure S A,B.C
=speed =speed =s'eed =speed
of of of of
sound sound sound sound and
-salinity,
in in in in
seawater water, pure water, seawater at zero pressure, pure water at zero pressure,
=coefficients
Solving for S, the equation can rearranged as C*S^2 +B*S'^1.5 +A*S or
S^2
+
+ (uO-uOpure)
(u -upure)
a*S'^l.5
b*S
+
+
d
0.
=0
# include "'math.h t 1.0e-06 1.0e-10
# define EPSi # define EPS2
double sfsvel( u, t, p double u; double t; double p;
/* sound velocity in rn/s /* temperature in deg. C /* pressure in dbars ~
* *
double sqrto; double u_pure; double a, b, d, factor, 5, si, s2, s3, s3_old, fO, fl, f2, f3; int flag = 1; /*------- initialize parameter coefficients----------* double double double double double double double
ul = 1402.388, u4 = 3.3420e-4, u7 = 0.153563, ulO =l.3621e-7, u13 = -1.7107e-6, u16 = 1.0405e-12, u19 = -2.3643e-12;
double dl double d4 double d7
= = =
double al double a4 double a7
= = =
F2
1.389, 2.006e-6, -4.42e-5, 9.4742e-5, 1.0507e-8,
9.104le-9,
TR 8920
u2 u5 uS ull u14 u17
= = = = = =
5.03711, -1.47800e-6, 6.8982e-4, -6.1185e-10, 2.5974e-8, -9.7729e-9,
u3 = -5.80852e-2; u6 =3.1464e-9; u9 = -8.1788e-6; u12 = 3.1260e-5; u15 = -2.5335e-10; ulB = 3.8504e-10;
d2 d5 d8
= = =
-1.262e-2, -3.2le-8,
d3 d6
= =
7.164e-5; -1.922e-2;
a2 a5 a8
= = =
-1.2580e-5, -2.0122e-10, -1.6002e-10,
a3 a6 a9
= = =
-6.4885e-8; -3.9064e-7; 7.988e-12;
1.727e-3;
double alO =l.100e-l0,
all
=
6.649e-12,
a12
=
-3.389e-13;
double bl
b2
=
1.7945e-7,
ci
=
-7.9836e-6;
7.3637e-5,
=
/*-------------------------------------------------------------* p 1 /*
10.;
/*-- convert dbars to bars
compute the speed of sound in pure water (Chen & Millero, Eq (3)--*
--
upure
=
ul
t*( t*( t*( t*(
+ + + ( u12 + + ( u17 + * ( u7
factor a a
-
u2 u8 u13 u18
+ + + +
t*( u3 + t*( u4 + t*( u5 + t*uE)))) t*( u9 + t*( u10 + t*ull))fl*p t*( u14 + t*( u15 + t*u16))))*p*p t*u19))*p*p*p;
+ d8;
=cl*p
d6 + t*d7)
+ (bl +t*b2
*p;
1=factor;
b
dl +t*( d2 + t*(d3 +t*(d4 +t*d5))
=
+ (al +t*( a2 +t*(a3 +t*( a4 +t*a5))))*p + (a6 + t*( a7 + t*( a8 + t*a9)))*p*p + (alO + t*( all + t*a12 ))*p*p*p;
1=factor;
b d
=uypure
-
u;
1=factor;
d
1* Need to solve equation
S^2 + a*S~l.5 + b*S + d with the desired root between S = 0 and S = 40.
=0
Solution is obtained by modified linear interpolation method as shown in "Applied Numerical Analysis (Second Edition)" by C.F. Gerald, Addison-Wesley Publishing Company, 1978, 518p. sl= s2 = fl = f2 = fo =
*
0.;
40.; sl*sl + a*sl*sqrt( si + b'~sl + d; s2*s2 + a*s2*sqrt( s2 )+ b*s2 + d; fl;
s3 = si; s3_old =s2; if( fl != 0. H( while(C flag 1=I s3 = s2 - f2*( s2 -1 )/(Mf2 - fl if( s3 < 0. ) return( atof( "-l.e30", ) ; f3 = 3*s3 + a*s3*sqrt( s3 )+ b*s3 + d; if( f3/fl < 0. ) s2 = s3; f2 =f3; if( f3/fO > 0. )fl *= 0.5;
*
--
return bad value *
else( si = s3; fli f3; if( f3/fO > 0. 1f2 *= 0.5; fO =f3; if( fabs( s3 S5 s3; break;
-
s3 old )
